Proceedings of the Asia-Pacific Microwave Conference 2016 MTM: Casimir Effect and Gravity Wave Detection Ulrich L. Rohde #1,2, Ajay Poddar *1, Shiban K. Koul #3 # Synergy Microwave Corp., Research & Development, 201 McLean Blvd., Paterson NJ 07504, USA * Brandenburg Technical University, Faculty of Electrical Engineering, Cottbus 03046, Germany # Indian Institute of Technology Delhi, Centre of Applied Research, New Delhi, India [email protected]; [email protected]; [email protected] Abstract-MTM (Metamaterial) is a negative index composite MTM a non-homogeneous material structure, characterized structure, involves multi-disciplinary engineering challenges and by effective constitutive parameters: εr = n/z, µr = n×z, which opportunity. This paper reports MTM inspired structure for analyzing and Casimir effect and GW (Gravity Wave) detection. gives a direct logical explanation of medium. However, determination of wave impedance ‘z’ (normalized impedance) I. INTRODUCTION of MTM structure is challenging because it’s value depends on MTM (Metamaterial) is an artificial composite structure, surface termination and overall size of the structure [1]. exhibits negative index (=−√ ; ε < 0, µ < 0, where is We can possibly determine index (n) and wave impedance refractive index, ε is electric permittivity of medium, and µ is (z) of non-homogeneous periodic MTM structure but requires , magnetic permeability of medium) characteristics. Figure (1) prior information about termination of unit cell, phases and shows the typical characteristics of the medium that explains amplitudes of the transmitted/reflected wave from the MTM the properties of natural and artificially engineered composite structure. The problem is if the structures are not symmetric material [1]. Figure (2) shows the MTM inspired Grapheme along the wave propagation direction, lead to two different nano-ribbons, which possess topology-induced desirable high values of ‘z’ corresponding to two incident directions of Q-factor components and desirable electromagnetic properties. propagation. This creates uncertainty in the computation of ‘z’, Unlike conventional materials, which interact with EM ε and µ, increases as the ratio of MTM unit cell size to (electromagnetic) wave based on their chemical composition, wavelength increases [2]-[3]. the properties of NIM (negative index material), and known as II. RETRIEVAL OF MTM’S EFFECTIVE PARAMETERS (, ) MTM come from their geometric topology structure. SRR (Split Ring Resonator) is considered as a simplest unit MTM cell. Figure (3) shows the typical SRR unit cell structure for a theoretical formulation that gives brief insights about physical properties and geometrical parameters. The analytical values of constitutive parameters (, , ) is given by =1+ +4 (1) =1+ (2) =− −2 (3) Fig. 1: A typical representation of the medium: 3rd quadrant explains left- handed medium, NIM (negative index) material properties [1] where =+, = , =++/2 and =+ 2 + ; L and are SRR total inductance and capacitance between the rings. As depicted in Figure (3), SRR acts as a resonant LC circuit, frequency of the resonance is given by = (4) L and is given by analytical equations [4]. Cgap is the capacitance of the gap illustrated in Figure (3), for narrow gap, its capacitance can be theoretically estimates reported in [5] = + with = ℎ++) (5) For example, the dimension of SRR is: a = 3 mm, r = 0.74 mm, c = 0.2 mm, s = 0.1 mm, g = 0.2 mm, t = 0.3 mm, h = 35 -12 -9 µm, ε0=8.8541×10 F/m. From (1)-(5), L = 3:9287× 10 H, -11 -15 Fig.2: Möbius-Strips structure formed by Grapheme nanoribbons exhibits Cpul = 1:6806 × 10 F, Cgap = 4:155 × 10 F and R = 0:4901 negative index properties (ε<0, µ<0), well suited suitable for high quality Ω at the frequency of resonance. factor microwave frequency components 978-1-5090-1592-4/16/$31.00 ©2016 IEEE In general, Casimir forces between macroscopic surfaces entail separations typically > 0.1um where retardation plays an essential role, while van der Waals forces refer to separations < 0.01um where retardation is insignificant. Figure (4) shows the practical evidence of Casimir force ‘F’ on parallel plates kept in vacuum, the effective force F ∝A/d4, where A is the area of plate and d is the distance between the plates [12]. Advances in theoretical studies and experimental techniques have enabled examination of the Casimir force beyond the Fig. 3: A typical SRR unit cell shows the asymmetric rings original configuration of two parallel perfect metal plates. Novel materials and shapes of the interacting bodies enable The numerical values obtained using (1)-(5) are new opportunities for applications and, at the same time, pose approximate, resulting poor accuracy of analytical method, new open questions. On the theoretical side, MTM-Inspired errors increases for thicker structures. The alternative structure can produce a powerful Casimir Effect, which will technique is based on S-parameters extraction. allow us to transport the matter; this implies that we can use There are three imperative methods generally used for the this effect to attract or push away physical matter in principle. determination of effective constitutive parameters based on The significantly greater complexity of the Casimir force applications and acceptable limit of errors [3]. potentially allows greater opportunity for neutralization or for The first method is to numerically calculate the ratios of the use of Casimir forces to partially cancel Van Der Waals forces. EM (electromagnetic) field inside MTM’s structure but this Figure (5) depicts the polaritonic characteristics of the Casimir approach is good for numerical simulations, and not for effect between conventional Metal and MTM structure. It can experimental measurement [6]. The second method calculates be seen that polaritonic involvement causes repulsive Casimir the effective constitutive parameters by using analytical force between Metal and MTM structure. For example, L ≥ models of MTM’s structures including numerical averaging of λ /5 binding TM polariton govern at shorter distance, fields. But this technique also not suitable for complex r inundated by joint repulsion due to anti-binding TM and TE structures such as superconducting MTM. The third method is polaritons. This explains that for a hybrid arrangement, surface a retrieval technique based on the inversion of scattering data plasmons are decisive in determining strength and sign of the (S-parameters) of a finite slab, called the NRW (Nicolson– Casimir force of interactions. Figure (6) shows the typical Ross–Weir) procedure [7]-[9]. The problem with NRW example of levitating mirror (The repulsive Casimir force of a method arises in case when topology driven MTM’s structure Metamaterial may balance the weight of one of the mirrors, undergo asymmetric reflections. Smith et al. [2] reported a letting it levitate on zero-point fluctuation). modified approach to resolve asymmetric reflections concern with the help of averaged value of reflection coefficients. As we know that isotropic medium model cannot replace this property, hence it is important to understand the EM dynamics of SR inspired MTM medium that intrinsically possess reflection asymmetric structures (S11 ≠S22) [10]. III. MTM: EMERGING APPLICATIONS The promising opportunity is in the area of detection of weak signal and signal processing where the space-time cloak serves as a means of prioritizing data channels, instead of Fig.4. Repulsive Casimir force ‘F’ on parallel plate kept in vacuum, effective theoretically effort to combine space-time and spatial cloaks. force F ∝- A/d4, A is the area of plate, d is the distance between the plates. The topology inspired Möbius transformation [11] MTM structure is attention-grabbing for a relativistic case, including Casimir force of attraction/repulsion in vacuum. A. Casimir Effect (Force from nothing) The Casimir force as illustrated in Figure (4) originates from the interaction of the surfaces with the surrounding electromagnetic spectrum, exhibits dependence on dielectric properties of surfaces and the medium between. Casimir forces between macroscopic surfaces have the same physical origin as atom-surface interactions and those between two atoms or molecules (van de Waals forces), because they originated from quantum fluctuations. Fig. 5: Typical polaritonic plots between Metal and MTM -Inspired mirror. The explanation of anti-gravity or levitation effect One of the fascinating information about “dark energy” is illustrated in Figure (6) can be given based on analogy that it seems to act with enormous force over the vast empty vibration modes of violin strings in acoustics. In acoustics, spaces in our universe, pushing space apart, while not having vibration of a violin strings broken down into a grouping of any measurable effect on the scale of planets or even the solar normal modes of oscillation, defined by the distance between system. The adaptive nature suggests that ‘dark energy’ is a the ends of the string. Similarly, oscillating EM fields can also particle which interacts stalwartly in a vacuum, while being be described in terms of these modes such as different screened in 'denser' medium such as on Earth or Milky Way. possible standing wave fields in a vacuum inside metal box. C. Casimir Effect: Detection of GW (Gravitational Wave) According to classical theory, if there is no field in the box, no One of the exciting properties